Terahertz radiation is a form of electromagnetic radiation that in frequency or wavelength is in that part of the electromagnetic spectrum that lies between the microwave region on the low frequency side and infrared radiation on the high frequency side. A generally accepted definition of what constitutes the terahertz band of frequencies is those frequencies extending from 0.5 THz to 10 THz, where 1 THz=1012 Hz.
Many important applications are foreseen for terahertz radiation, for example in security monitoring, non-destructive testing, process monitoring, biosensors, medical hyperspectral imaging, material characterization, communications; as well as spectroscopic and imaging applications in the sciences, including the physical and bio-sciences, and engineering. However, practical sources and detectors are not yet readily available. In part, this is because electronic-based sources extend in frequency coverage up to the lower end of the terahertz range, whereas photonic sources extend downwards towards the upper end of the terahertz range.
In recent years substantial progress has been made in addressing these shortfalls. Current techniques for generating terahertz radiation include the use of quantum cascade lasers, femto-second lasers, parametric generators, and difference frequency generators. However, some of the most promising detectors rely on the electro-optic effect. The electro-optic effect arises when an electric field is applied to a suitable material to change its optical properties, in particular inducing birefringence in the material. For the linear electro-optic or Pockels effect, the one under consideration herein, the change in refractive index and hence the birefringence induced in the material, is linearly proportional to the inducing electric field. Such changes can be measured by propagating a probe beam through the electro-optic medium and measuring changes in its polarization state. When the inducing electric field is the electric field of the terahertz radiation itself, the change thereby measured is directly proportional to the magnitude of the electric field of the terahertz radiation.
The larger the electro-optic coefficient of the material the larger the birefringence induced in the material. In order to maximize the effect of the induced birefringence on the probe radiation, the probe radiation must be phase-matched with the terahertz radiation as they propagate through the material. Where the terahertz radiation is in the form of nanosecond pulses, this phase matching is accomplished by matching the phase velocity of the probe radiation in the electro-optic medium to the phase velocity of the terahertz radiation in this medium. This may be accomplished by suitable choice of both the electro-optic medium and the wavelength of the probe.
FIG. 1 explains this principle of phase matching. The upper trace in this figure shows the sinusoidal variation of the electric field strength of the terahertz radiation in the electro-optic medium, in particular illustrating that the direction of this electric field changes from positive to negative within each half cycle of the terahertz radiation, where λ(THz) is the wavelength and V(THz) the phase velocity of the terahertz radiation in the medium. In the lower section of the diagram, is illustrated a number of sequential wavefronts associated with the probe radiation, each separated from the next by the wavelength of the probe radiation in the electro-optic medium. These particular wavefronts are shown as being subjected at the particular identified point in the medium to the (maximum) positive (red arrow) electric field of the terahertz radiation.
In order to ensure that the illustrated wavefronts experience the maximum total induced birefringence as they propagate throughout the full length of the medium then they must continue to experience as they propagate this maximum positive electric field at all points within the medium. It will be apparent that this will be the case if the phase velocity V(probe) of the probe radiation in the medium is equal to the phase velocity V(THz) of the terahertz radiation in the medium. If on the other hand they experience an electric field that changes from positive to negative on their propagation through the medium, the birefringence induced by the positive field would be cancelled or partially cancelled by the birefringence induced by the negative field. In practice, it may not always be possible to attain perfect phase matching thereby placing an upper limit on the maximum path length over which the probe radiation can effectively interact with the terahertz radiation.
In practice, the upper limit on the path length within the electro-optic medium over which optical birefringence may be induced is caused by absorption of the terahertz radiation by the electro-optic medium. This in turn places an upper limit on the path length over which such birefringence is induced to affect the polarization state of the probe radiation. By way of example only, a widely adopted material for electro-optic detection of THz radiation is ZnTe, chosen because of its favourable combination of electro-optic, transmission and phase-matching properties. Typically both phase matching and THz wave absorption limit the thickness of the ZnTe crystal that can be used to less than 1-2 mm. On the other hand, the absorption of the radiation used to probe the electro-optic effect is a much less severe limitation and therefore not significant provided the wavelength of this radiation exceeds 600 nm.
Although electro-optic techniques are now well established for femto-second pulses of terahertz radiation and continuous-wave generation of terahertz radiation, this is not the case in the intermediate region between ultrashort pulses and continuous wave, and in particular for nanosecond pulses of terahertz radiation, since in this region the lower electric field strengths encountered cannot be readily compensated by coherent detection techniques.